Due to cold weather a 1m water pipe of cross-sectional area 1cm^2 is filled with ice at -10^0C. Resistive heating is used to melt the ice. Current 0.5A of is passed through 4 k Ω resistance. Assuming…

Question

Due to cold weather a 1m water pipe of cross-sectional area

1 c m^{2}

is filled with ice at -

1 0^{0}

C. Resistive heating is used to melt the ice. Current 0.5A of is passed through

4 k Ω

resistance. Assuming that all the heat produced is used for melting, what is the minimum time required?
(Given latent heat of fusion for water/ice

= 3.33 \times 1 0^{5} J k g^{- 1}

, specific heat of ice

= 2 \times 1 0^{3} J k g^{- 1}

and density of ice

= 1 0^{3} k g / m^{3}

)

Accepted Answer

Correct answer: B. (b) mass of ice m= ρAl=10^3 10^-4 1=10^-1 kg Energy required to melt the ice Q = ms ∆T + mL = 10−1(2 × 103 × 10 + 3.33 × 105) = 3.53 × 104 J Q = i2RT 3.53 × 104 = ( 12 )^2(4 10^3) (t ) Time = 35.3sec

Solution

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